Question

For what value of C will y = sin(x - C) be an even function? a. 2π b. π c. π/2

Answer 1

Answer:

c.$\frac{\pi}{2}$

Step-by-step explanation:

We are given that

$y=sin(x-C)$

We have to find the  value of C for which  given function is even function.

We know that

Even function : If f(x)=f(-x) then the function is called even function.

$a.2\pi$

Substitute the value then we get

$y= sin(x-2\pi)= sin(-(2\pi-x))=-sin (2\pi-x)=sin x$

We know that sin (-x)=-sin x, $sin(2\pi-x)=-sinx$

We know that Sin x is an odd function , therefore, option a is incorrect.

b.$\pi$

Substitute the value then we get

$y= sin (x-\pi)=sin(-(\pi-x))=-sin (\pi-x)=-sin x$

It is an odd function.

Hence, option b is incorrect.

c.$\frac{\pi}{2}$

Substitute the value then we get

$y= sin(x-\frac{\pi}{2})=sin(-(\frac{\pi}{2}-x))=-sin(\frac{\pi}{2}-x)=-cos x$

$sin(\frac{\pi}{2}-x)=cosx$

We know that cos x is even function

Replace x by -x then, we get

$-cos (-x)=-cos x$....(cos (-x)=cos x)

Hence, the value of C=$\frac{\pi}{2}$  for which given function will be an even function.

Answer:c.$\frac{\pi}{2}$

Answer 2

Answer:

you are actually incorrect the answer is  2π